Actually even sword masters would avoid using two weapons at once, because the amount of coordination and extra brain-processing it requires would ruin any truly deadly skill. Unless you use the second weapon mainly as stopper, like a very poor shield. But you still are thinking during tight situations: "should I use my second weapon now?".
Your mass balance is worse, too. Probably you'll lose some fingers on your left hand when trying to stop blows with a long dagger or something like that. Who in ancient warfare, or even assasin missions, did use two weapons?
Roman army actually had enough with one short sword and a big shield, so it's not the way to go to be a deadly fighter.

